Model based clustering of multinomial count data

The parsimonious Gaussian mixture models, which exploit an eigenvalue decomposition of the group covariance matrices of the Gaussian mixture, have shown their success in particular in cluster analysis. Their estimation is in general performed by maximum likelihood estimation and has also been considered from a parametric Bayesian prospective. We propose new Dirichlet Process Parsimonious mixtures (DPPM) which represent a Bayesian nonparametric formulation of these parsimoniou...

Choosing the number of mixture components remains an elusive challenge. Model selection criteria can be either overly liberal or conservative and return poorly-separated components of limited practical use. We formalize non-local priors (NLPs) for mixtures and show how they lead to well-separated components with non-negligible weight, interpretable as distinct subpopulations. We also propose an estimator for posterior model probabilities under local and non-local priors, show...

In this paper, we study different discrete data clustering methods, which use the Model-Based Clustering (MBC) framework with the Multinomial distribution. Our study comprises several relevant issues, such as initialization, model estimation and model selection. Additionally, we propose a novel MBC method by efficiently combining the partitional and hierarchical clustering techniques. We conduct experiments on both synthetic and real data and evaluate the methods using accura...

Clustering is an important task in many areas of knowledge: medicine and epidemiology, genomics, environmental science, economics, visual sciences, among others. Methodologies to perform inference on the number of clusters have often been proved to be inconsistent, and introducing a dependence structure among the clusters implies additional difficulties in the estimation process. In a Bayesian setting, clustering is performed by considering the unknown partition as a random o...

Bayesian nonparametric mixture models are common for modeling complex data. While these models are well-suited for density estimation, their application for clustering has some limitations. Miller and Harrison (2014) proved posterior inconsistency in the number of clusters when the true number of clusters is finite for Dirichlet process and Pitman--Yor process mixture models. In this work, we extend this result to additional Bayesian nonparametric priors such as Gibbs-type pr...

In model-based-clustering mixture models are used to group data points into clusters. A useful concept introduced for Gaussian mixtures by Malsiner Walli et al (2016) are sparse finite mixtures, where the prior distribution on the weight distribution of a mixture with $K$ components is chosen in such a way that a priori the number of clusters in the data is random and is allowed to be smaller than $K$ with high probability. The number of cluster is then inferred a posteriori ...

In the framework of Bayesian model-based clustering based on a finite mixture of Gaussian distributions, we present a joint approach to estimate the number of mixture components and identify cluster-relevant variables simultaneously as well as to obtain an identified model. Our approach consists in specifying sparse hierarchical priors on the mixture weights and component means. In a deliberately overfitting mixture model the sparse prior on the weights empties superfluous co...

Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare different mixture models using penalized log-likelihood criteria such as BIC.We propose fitting MLMMs with variational methods which can perform parameter estimation and model selection simultaneously. A variational approximation is describ...

Bayesian nonparametric mixture models are widely used to cluster observations. However, one major drawback of the approach is that the estimated partition often presents unbalanced clusters' frequencies with only a few dominating clusters and a large number of sparsely-populated ones. This feature translates into results that are often uninterpretable unless we accept to ignore a relevant number of observations and clusters. Interpreting the posterior distribution as penalize...

The intricacies inherent in contemporary real datasets demand more advanced statistical models to effectively address complex challenges. In this article we delve into problems related to identifying clusters across related groups, when additional covariate information is available. We formulate a novel Bayesian nonparametric approach based on mixture models, integrating ideas from the hierarchical Dirichlet process and "single-atoms" dependent Dirichlet process. The proposed...